How to procedurally deform shape of an object?
Add a Displace modifier to the object, set the texture coordinates to "object". Add an empty and set it in the object field. Set the strength to a low value (0.1 for example) and set the direction to "RGB to XYZ".
Add a texture in the modifer, and click on the far right icon of the texture field, alternatively click on the checker icon on the bottom of the properties.



Set The texture type to clouds, and the color from grayscale to color. Up the size a little bit. (depends on the real scale of your object)



If your object doesn't deform correctly, you should make sure to have a dense enough mesh. Add a subdivision modifier before the displace modifier and set the divisions to 1 or 2.

Now move your empty object in the scene and the object should deform.